System and Method for Inspection Using Tensor Decomposition and Singular Value Decomposition

ABSTRACT

A sample characterization system is disclosed. In embodiments, the sample characterization system includes a controller communicatively coupled to an inspection sub-system, the controller including one or more processors configured to execute a set of program instructions stored in memory, the set of program instructions configured to cause the one or more processors to: acquire one or more target image frames of a sample; generate a target tensor with the one or more acquired target image frames; perform a first set of one or more decomposition processes on the target tensor to form generate one or more reference tensors including one or more reference image frames; identify one or more differences between the one or more target image frames and the one or more reference image frames; and determine one or more characteristics of the sample based on the one or more identified differences.

CROSS-REFERENCE TO RELATED APPLICATION

The present application claims the benefit under 35 U.S.C. § 119(e) ofU.S. Provisional Application Ser. No. 62/797,581, filed Jan. 28, 2019,entitled DEFECT INSPECTION USING TENSOR DECOMPOSITIONS, naming RichardWallingford as inventor, and U.S. Provisional Application Ser. No.62/905,063, filed Sep. 24, 2019, entitled PATTERN NOISE REMOVAL USINGSINGULAR VALUE DECOMPOSITION TO INCREASE SENSITIVITY OF BRIGHTFIELDWAFER INSPECTION TOOLS, naming Nurmohammed Patwary, James A. Smith,Xiaochun Li, Richard Wallingford, Vladimir Tumakov, and Bjorn Brauer asinventors, both of which are incorporated herein by reference in theentirety.

TECHNICAL FIELD

The present invention generally relates to semiconductor waferfabrication and characterization and, more particularly, to a system andmethod for improved semiconductor inspection using tensor decompositionsand singular value decomposition (SVD) processes.

BACKGROUND

Demand for electronic logic and memory devices with ever-smallerfootprints and features present a wide range of manufacturing challengesbeyond fabrication at a desired scale. In the context of semiconductorfabrication, accurately identifying the type and size of defects is animportant step in improving throughput and yield. Some conventionalinspection techniques identify defects on a region of a sample (e.g., ona die of the sample) by comparing images of the die with images ofadjacent die of the sample (“die-to-die”). Similarly, other conventionalinspection techniques may identify defects on a die of a sample bycomparing images of the die against a robust estimation of a referenceimage constructed from multiple neighboring die (“die-to-median die” or“die to computed reference die”).

Using these conventional inspection techniques, the comparison of therespective images is typically carried out by subtraction after suitablesub-pixel alignment of all die used for the computation is performed.The subtraction operation between the images is intended to remove mostof the intrinsic pattern of the sample, leaving any defect signals andresidual noise components. The defect may then be detected if the defectsignal value exceeds that of the residual noise signal. However, theseconventional inspection techniques may include additional noise fromadjacent reference imagery, leading to decreased sensitivity. Forexample, die-to-die inspection techniques may include process variationerrors and alignment errors between the target die and the referencedie. The use of more robust reference imagery in die-to-median dieinspection techniques and/or die-to-computed reference die inspectiontechniques may reduce these process variation and alignment errors, butnot to a degree which is suitable for many inspection processes.

Therefore, it would be desirable to provide a system and method whichcures one or more of the shortfalls of previous approaches identifiedabove.

SUMMARY

A sample characterization system is disclosed. In embodiments, thesample characterization system includes a controller communicativelycoupled to an inspection sub-system, the controller including one ormore processors configured to execute a set of program instructionsstored in memory, the set of program instructions configured to causethe one or more processors to: acquire one or more target image framesof a sample; generate a target tensor with the one or more acquiredtarget image frames; perform a first set of one or more decompositionprocesses on the target tensor to form generate one or more referencetensors including one or more reference image frames; identify one ormore differences between the one or more target image frames and the oneor more reference image frames; and determine one or morecharacteristics of the sample based on the one or more identifieddifferences.

A method for characterizing a sample is disclosed. In embodiments, themethod includes: acquiring one or more target image frames of a sample;generating a target tensor with the one or more acquired target imageframes; performing a first set of one or more decomposition processes onthe target tensor to generate one or more reference tensors includingone or more reference image frames; identifying one or more differencesbetween the one or more target image frames and the one or morereference image frames; and determining one or more characteristics ofthe sample based on the one or more identified differences.

A sample characterization system is disclosed. In embodiments, thesample characterization system includes a controller communicativelycoupled to an inspection sub-system, the controller including one ormore processors configured to execute a set of program instructionsstored in memory, the set of program instructions configured to causethe one or more processors to: acquire one or more difference imageframes of a sample, the one or more difference image frames based on oneor more target image frames and one or more reference image frames;generate one or more stacked difference images with the one or moreacquired difference image frames; perform a set of one or more singularvalue decomposition (SVD) processes on the one or more stackeddifference images to form a set of one or more singular vectors;selectively modify at least one singular vector of the set of one ormore singular vectors to generate a modified set of one or more singularvectors; generate a modified stacked difference image based on themodified set of one or more singular vectors; and determine one or morecharacteristics of the sample based on the modified stacked differenceimage.

A method for characterizing a sample is disclosed. In embodiments, themethod includes: acquiring one or more difference image frames of asample, the one or more difference image frames based on one or moretarget image frames and one or more reference image frames; generatingone or more stacked difference images with the one or more acquireddifference image frames; performing a set of one or more singular valuedecomposition (SVD) processes on the one or more stacked differenceimages to form a set of one or more singular vectors; selectivelymodifying at least one singular vector of the set of one or moresingular vectors to generate a modified set of one or more singularvectors; generating a modified stacked difference image based on themodified set of one or more singular vectors; and determining one ormore characteristics of the sample based on the modified stackeddifference image.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not necessarily restrictive of the invention as claimed. Theaccompanying drawings, which are incorporated in and constitute a partof the specification, illustrate embodiments of the invention andtogether with the general description, serve to explain the principlesof the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The numerous advantages of the disclosure may be better understood bythose skilled in the art by reference to the accompanying figures inwhich:

FIG. 1 illustrates a characterization system for performing inspection,in accordance with one or more embodiments of the present disclosure.

FIG. 2 illustrate a flowchart of a method for performing inspectionusing tensor decomposition processes, in accordance with one or moreembodiments of the present disclosure.

FIG. 3 illustrates a flowchart for generating a target tensor fromtarget image frames of a sample, in accordance with one or moreembodiments of the present disclosure.

FIG. 4 illustrates a simplified block diagram of a decomposition processperformed on a target tensor, in accordance with one or more embodimentsof the present disclosure.

FIG. 5 illustrates a simplified block diagram of a decomposition processperformed on a target tensor, in accordance with one or more embodimentsof the present disclosure.

FIG. 6A illustrates a target image frame of a target tensor, inaccordance with one or more embodiments of the present disclosure.

FIG. 6B illustrates a reference image frame of a reference tensor, inaccordance with one or more embodiments of the present disclosure.

FIG. 6C illustrates a difference image frame, in accordance with one ormore embodiments of the present disclosure.

FIG. 7A illustrates a difference image frame generated by a conventional“die-to-die” or “cell-to-cell” inspection technique.

FIG. 7B illustrates a difference image frame generated by a conventional“die-to-median die” or “cell-to-median cell” inspection technique.

FIG. 8 illustrate a flowchart for performing inspection using tensordecomposition processes and de-noising processes of a target tensor, inaccordance with one or more embodiments of the present disclosure.

FIG. 9 illustrate a flowchart of a method for performing inspectionusing singular value decomposition (SVD) processes, in accordance withone or more embodiments of the present disclosure.

FIG. 10 illustrates a flowchart of a method for performing inspectionusing singular value decomposition (SVD) processes, in accordance withone or more embodiments of the present disclosure.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to the subject matter disclosed,which is illustrated in the accompanying drawings.

Referring generally to FIGS. 1-110, a system and method for inspectionof semiconductor devices utilizing tensor decomposition and singularvalue decomposition (SVD) processes are described, in accordance withone or more embodiments of the present disclosure.

Some conventional inspection techniques identify defects on a region ofa sample (e.g., on a die of the sample) by comparing images of the diewith images of adjacent die of the sample (“die-to-die”). Similarly,other conventional inspection techniques may identify defects on a dieof a sample by comparing images of the die against a robust estimationof a reference image constructed from multiple neighboring die(“die-to-median die” or “die to computed reference die”). For example,conventional inspection techniques may compare target images (e.g.,images of die under inspection) to reference images of adjacent die toform difference images. The difference images may then be used toidentify defects of the sample within the target die. Reference imagesmay be formed using a number of techniques, including left and rightadjacent die to the target with double detection (MDAT1), median ofadjacent reference die (MDAT2 or PVS), computed reference die (e.g.,optimal linear combination of die along a die row), and the like.

Using these conventional inspection techniques, the comparison of therespective images is typically carried out by subtraction after suitablesub-pixel alignment of all die used for the computation is performed.The subtraction operation between the images is intended to remove mostof the intrinsic pattern of the sample, leaving any defect signals andresidual noise components. The defect may then be detected if the defectsignal value exceeds that of the residual noise signal. However, theseconventional inspection techniques may include additional noise fromadjacent reference imagery, leading to decreased sensitivity. Forexample, die-to-die inspection techniques may include process variationerrors and alignment errors between the target die and the referencedie. The use of more robust reference imagery in die-to-median dieinspection techniques and/or die-to-computed reference die inspectiontechniques may reduce these process variation and alignment errors, butnot to a degree which is suitable for many inspection processes.

Accordingly, embodiments of the present disclosure are directed to asystem and method which cure one or more shortfalls of the previousapproaches identified above. Embodiments of the present disclosure aredirected to a system and method for detecting defects on semiconductorwafers (e.g., samples) which offer improved sensitivity overconventional inspection techniques. In particular, embodiments of thepresent disclosure are directed to a system and method for generating anew type of reference image for inspection comparison operations whichmay lower residual noise, and thereby enhance defect detectionsensitivity. Some embodiments of the present disclosure are detected toa system and method for inspection of semiconductor devices utilizingtensor decomposition and singular value decomposition (SVD) processes.

FIG. 1 illustrates a characterization system 100 for performinginspection, in accordance with one or more embodiments of the presentdisclosure. In particular, FIG. 1 illustrates a system 100 for comparingtarget image frames 125 and reference image frames 135 usingdecomposition process in order to identify defects on a sample 120.

In embodiments, the system 100 may include an inspection sub-system 102.The inspection sub-system 102 may include any optical-basedinspection/characterization system or tool known in the art including,but not limited to, an image-based metrology tool, a review tool, andthe like. For example, the inspection sub-system 102 may include anoptical dark-field inspection tool and/or an optical bright-fieldinspection tool. The inspection sub-system 102 may include, but is notlimited to, an illumination source 112, an illumination arm 111, acollection arm 113, and a detector assembly 126.

In one embodiment, inspection sub-system 102 is configured to inspectand/or measure the sample 120 disposed on the stage assembly 122.Illumination source 112 may include any illumination source known in theart for generating illumination 101 including, but not limited to, abroadband radiation source (e.g., Xenon lamp, a laser-sustained plasma(LSP) illumination source), a narrowband illumination source (e.g.,laser illumination source), and the like. The illumination source 112may be configured to generate DUV, UV, VUV, and/or EUV illumination. Forinstance, the EUV illumination source may include a discharge producedplasma (DPP) illumination source or a laser produced plasma (LPP)illumination source configured to generate illumination in the EUVrange. By way of another example, the illumination source 112 may beconfigured to generate X-ray radiation. In another embodiment, theillumination source 112 may be operably coupled to a set of positionersconfigured to actuate the illumination source 112 in one or moredirections. For example, a controller 104 may direct the set ofpositioners to translate the illumination source 112 in one or more ofan X-direction, a Y-direction, and/or a Z-direction to correct beammisalignment produced by any of the components of the system 100.

In another embodiment, inspection sub-system 102 may include anillumination arm 111 configured to direct illumination 101 to the sample120. It is noted that illumination source 112 of inspection sub-system102 may be configured in any orientation known in the art including, butnot limited to, a dark-field orientation, a light-field orientation, andthe like. For example, the one or more optical elements 114, 124 may beselectably adjusted in order to configure the inspection sub-system 102in a dark-field orientation, a bright-field orientation, and the like.

Sample 120 may include any sample known in the art including, but notlimited to, a wafer (e.g., semiconductor wafer), a reticle, a photomask,and the like. As used through the present disclosure, the term “wafer”refers to a substrate formed of a semiconductor and/or anon-semiconductor material. For instance, in the case of a semiconductormaterial, the wafer may be formed from, but is not limited to,monocrystalline silicon, gallium arsenide, and/or indium phosphide. Inanother embodiment, the sample 120 includes a photomask/reticle. Assuch, the terms “wafer,” “sample,” and “sample” may be usedinterchangeably in the present disclosure. Therefore, the abovedescription should not be interpreted as a limitation on the scope ofthe present disclosure but merely an illustration.

In one embodiment, sample 120 is disposed on a stage assembly 122 tofacilitate movement of sample 120. In another embodiment, the stageassembly 122 is an actuatable stage. For example, the stage assembly 122may include, but is not limited to, one or more translational stagessuitable for selectably translating the sample 120 along one or morelinear directions (e.g., x-direction, y-direction and/or z-direction).By way of another example, the stage assembly 122 may include, but isnot limited to, one or more rotational stages suitable for selectivelyrotating the sample 120 along a rotational direction. By way of anotherexample, the stage assembly 122 may include, but is not limited to, arotational stage and a translational stage suitable for selectablytranslating the sample 120 along a linear direction and/or rotating thesample 120 along a rotational direction. It is noted herein that thesystem 100 may operate in any scanning mode known in the art.

The illumination arm 111 may include any number and type of opticalcomponents known in the art. In one embodiment, the illumination arm 111includes one or more optical elements 114, a set of one or more opticalelements 115, a beam splitter 116, and an objective lens 118. In thisregard, illumination arm 111 may be configured to focus illumination 101from the illumination source 112 onto the surface of the sample 120. Theone or more optical elements 114 may include any optical elements knownin the art including, but not limited to, one or more mirrors, one ormore lenses, one or more polarizers, one or more beam splitters, waveplates, and the like.

In another embodiment, optical inspection sub-system 102 includes acollection arm 113 configured to collect illumination reflected orscattered from sample 120. In another embodiment, collection arm 113 maydirect and/or focus the reflected and scattered light to one or moresensors of a detector assembly 126 via one or more optical elements 124.The one or more optical elements 124 may include any optical elementsknown in the art including, but not limited to, one or more mirrors, oneor more lenses, one or more polarizers, one or more beam splitters, waveplates, and the like. It is noted that detector assembly 126 may includeany sensor and detector assembly known in the art for detectingillumination reflected or scattered from the sample 120.

In another embodiment, the detector assembly 126 of the opticalinspection sub-system 102 is configured to collect metrology data of thesample 120 based on illumination reflected or scattered from the sample120. The detector assembly 126 may include any detector assembly knownin the art including, but not limited to, photo-multiplier tubes (PMTs),charge coupled devices (CCDs), time-delay integration (TDI) cameras, orthe like. In another embodiment, the detector assembly 126 is configuredto transmit collected/acquired images/image frames (e.g., target imageframes 125) and/or metrology data to the controller 104.

In embodiments, the controller 104 may be communicatively coupled to thevarious components of the inspection sub-system 102. For example, thecontroller 104 may be operably coupled to the illumination source 112,the stage assembly 122, and/or the detector assembly 126. The controller104 of system 100 may include one or more processors 106 and memory 108.The memory 108 may include program instructions configured to cause theone or more processors 106 to carry out various steps of the presentdisclosure. In one embodiment, the program instructions are configuredto cause the one or more processors 106 to adjust one or morecharacteristics of the optical inspection sub-system 102 in order toperform one or more measurements of the sample 120.

In one embodiment, the one or more processors 106 may include any one ormore processing elements known in the art. In this sense, the one ormore processors 106 may include any microprocessor-type deviceconfigured to execute software algorithms and/or instructions. In oneembodiment, the one or more processors 106 may consist of a desktopcomputer, mainframe computer system, workstation, image computer,parallel processor, or other computer system (e.g., networked computer)configured to execute a program configured to operate the system 100, asdescribed throughout the present disclosure. It should be recognizedthat the steps described throughout the present disclosure may becarried out by a single computer system or, alternatively, multiplecomputer systems. Furthermore, it should be recognized that the stepsdescribed throughout the present disclosure may be carried out on anyone or more of the one or more processors 106. In general, the term“processor” may be broadly defined to encompass any device having one ormore processing elements, which execute program instructions from memory108. Moreover, different subsystems of the system 100 (e.g.,illumination source 112, electron beam source 128, detector assembly126, electron detector assembly 134, controller 104, user interface 110,and the like) may include processor or logic elements suitable forcarrying out at least a portion of the steps described throughout thepresent disclosure. Therefore, the above description should not beinterpreted as a limitation on the present disclosure but merely anillustration.

The memory 108 may include any storage medium known in the art suitablefor storing program instructions executable by the associated one ormore processors 106 and the data received from the inspection sub-system102. For example, the memory 108 may include a non-transitory memorymedium. For instance, the memory 108 may include, but is not limited to,a read-only memory (ROM), a random-access memory (RAM), a magnetic oroptical memory device (e.g., disk), a magnetic tape, a solid-state driveand the like. It is further noted that memory 108 may be housed in acommon controller housing with the one or more processors 106. In analternative embodiment, the memory 108 may be located remotely withrespect to the physical location of the processors 106, controller 104,and the like. In another embodiment, the memory 108 maintains programinstructions for causing the one or more processors 106 to carry out thevarious steps described through the present disclosure.

In one embodiment, a user interface 110 is communicatively coupled tothe controller 104. In one embodiment, the user interface 110 mayinclude, but is not limited to, one or more desktops, tablets,smartphones, smart watches, or the like. In another embodiment, the userinterface 110 includes a display used to display data of the system 100to a user. The display of the user interface 110 may include any displayknown in the art. For example, the display may include, but is notlimited to, a liquid crystal display (LCD), an organic light-emittingdiode (OLED) based display, or a CRT display. Those skilled in the artshould recognize that any display device capable of integration with auser interface 110 is suitable for implementation in the presentdisclosure. In another embodiment, a user may input selections and/orinstructions responsive to data displayed to the user via a user inputdevice of the user interface 110.

As noted previously, the controller 104 of system 100 may include one ormore processors 106 configured to execute a set of program instructionsstored in memory 108, the set of program instructions configured tocause the one or more processors 106 to carry out varioussteps/functions of the present disclosure. In one embodiment, theprogram instructions are configured to cause the one or more processors106 to adjust one or more characteristics of the inspection sub-system102 in order to perform one or more measurements of the sample 120. Byway of another example, the set of program instructions may beconfigured to cause the one or more processors 106 of the controller 104to: acquire one or more target image frames of a sample; generate atarget tensor with the one or more acquired target image frames; performa first set of one or more decomposition processes on the target tensorto form a core tensor; generate one or more reference tensors includingone or more reference image frames based on the core tensor; identifyone or more differences between the one or more target image frames andthe one or more reference image frames; and determine one or morecharacteristics of the sample based on the one or more identifieddifferences.

The various steps/functions carried out by the controller 104 may befurther shown and understood with reference to FIG. 2.

FIG. 2 illustrate a flowchart of a method 200 for performing inspectionusing tensor decomposition processes, in accordance with one or moreembodiments of the present disclosure. It is noted herein that the stepsof method 200 may be implemented all or in part by system 100. It isfurther recognized, however, that the method 200 is not limited to thesystem 100 in that additional or alternative system-level embodimentsmay carry out all or part of the steps of method 200.

In a step 202, one or more target image frames 125 of a sample 120 areacquired. For example, FIG. 3 illustrates a flowchart for generating atarget tensor 132 from target image frames 125 of a sample 120, inaccordance with one or more embodiments of the present disclosure. Asshown in FIG. 3, the controller 104 may be configured to acquire aplurality of target image frames 125 a-125 h of a sample 120. The targetimage frames 125 a-125 h may be received from any source known in theart including, but not limited to, the inspection sub-system 102,memory, a network, and the like. For example, the controller 104 may beconfigured to cause the inspection sub-system 102 to acquire one or moretarget image frames 125 a-125 h, and may then receive the one or moreacquired target image frames 125 a-125 h from the inspection sub-system102. In embodiments, the controller 104 may store the acquired targetimage frames 125 a-125 h in memory.

In embodiments, the target image frames 125 may be acquired across aplurality of regions across the sample 120. For example, as shown inFIG. 3, the target image frames 125 may be acquired across two die rowsacross the sample 120. In this example, one or more target image frames125 may be acquired of adjacent regions/portions of the sample 120. Thetarget image frames 125 may be acquired such that they each include dieof the sample 120 which are fabricated according to identical and/orsimilar design data. In this regard, as shown in FIG. 3, the pluralityof target image frames 125 may include similar and/or identicalpatterned features/structures formed on the sample 120.

In a step 204, a target tensor 130 (T) is generated with the one or moreacquired target image frames 125. For example, the controller 104 may beconfigured to generate a target tensor 130 utilizing the acquired targetimage frames 125 a-125 h. For instance, as shown in FIG. 3, thecontroller 104 may be configured to form the target tensor 130 bystacking the one or more target image frames 125 a-125 h. While FIG. 3illustrates forming the target tensor 130 using eight target imageframes 125 a-125 h, this is not to be regarded as a limitation of thepresent disclosure, unless noted otherwise herein. In this regard, thecontroller 104 may be configured to form the target tensor 130 using anynumber of target image frames 120 a-125 n.

In a step 206, a first set of one or more decomposition processes areperformed on the target tensor 130 (T) to form one or more referencetensors 136 (T_(B)) including one or more reference image frames. Thismay be further understood with reference to FIGS. 4 and 5.

FIG. 4 illustrates a simplified block diagram of a decomposition processperformed on a target tensor 130, in accordance with one or moreembodiments of the present disclosure.

In some embodiments, as shown in FIG. 4, decomposition of the targettensor 130 (T) may be described according to Equation 1:

T=SU ⁽¹⁾ U ⁽²⁾ U ⁽³⁾  (1)

wherein T defines the target tensor 130 made up of target image frames125 a-125 n, S defines a core tensor 132, U⁽¹⁾ defines an orthonormalbasis vector 134 a for a column space of the target tensor 130, U⁽²⁾defines an orthonormal basis vector 134 b for a row space of the targettensor 130, and U⁽³⁾ defines an orthonormal basis vector 134 c for a diespace (stack space) of the target tensor 130.

The set of one or more decomposition processes used to determine thecore tensor 132 (S) from the target tensor 130 (T) may include anydecomposition processes known in the art including, but not limited to,multi-linear decomposition processes. For example, in some embodiments,the set of decomposition processes performed in step 206 may include aTucker decomposition process. For instance, the set of decompositionprocesses performed in step 206 may include a multilinear singular valuedecomposition (SVD) process, as shown in FIG. 4. In some embodiments,the controller 104 is configured to perform the first set of one or moredecomposition processes on the target tensor 130 using the firstorthonormal basis vector 134 a (U⁽¹⁾) for a column space of the targettensor 130, a second orthonormal basis vector 134 b (U⁽²⁾) for a rowspace of the target tensor, and a third orthonormal basis vector 134 c(U⁽³⁾) for a stack space of the target tensor 130.

Tucker decomposition processes are described in greater detail by L. R.Tucker in The Extension of Factor Analysis to Three-DimensionalMatrices, Contributions to Mathematical Psychology, Hold, Rinehart andWinston, New York, 1964, which is incorporated herein by reference inthe entirety. Similarly, singular value decomposition (SVD) processesare described in greater detail by Lieven De Lathauwer, et al., in AMultilinear Singular Value Decomposition, SIAM J. Matrix Anal. Appl.,Vol. 21, No. 4, pp. 1253-1278 (2000), which is incorporated herein byreference in the entirety.

In embodiments, the controller 104 may be configured to generate areference tensor 136 which includes one or more reference image framesbased on the core tensor 132 (S). In this regard, the controller 104 maybe configured to generate one or more reference image frames based onthe core tensor 132 (S). In some embodiments, the controller 104 isconfigured to generate the one or more reference tensors 136 byperforming one or more low-rank approximations of the core tensor 132(S) generated via the multilinear decompositions. The controller 104 maybe configured to store generated reference tensors 136 (T_(B)) and/orreference image frames 155 in memory 108.

For example, the controller 104 may generate the reference tensor 136(and reference image frames) via a low-rank approximation by truncatingat least a portion of the core tensor 132 (S) and/or by truncating atleast a portion of at least one of the orthonormal basis vectors 134 a,134 b, 134 c (U⁽¹⁾, U⁽²⁾, U⁽³⁾). As opposed to a full-rankdecomposition, which would result in a reference tensor 136 (T_(B))which exactly represents the target tensor 130 S (within numericalprecision), a low-rank approximation may be performed in order toestimate the background pattern of the sample 120 using only lower-rankterms. This may be further understood with reference to FIG. 5.

FIG. 5 illustrates a simplified block diagram of a decomposition processperformed on a target tensor 130 (T), in accordance with one or moreembodiments of the present disclosure.

By way of example, the controller 104 may be configured to generate areference tensor 136 (T_(B)) (and reference image frames) via a low-rankapproximation by truncating a portion of the core tensor 132 (S) togenerate a truncated core tensor 133 (S_(B)). Similarly, the controller104 may be configured to truncate a portion of orthonormal basis vector134 a (U⁽¹⁾) and orthonormal basis vector 134 b (U⁽²⁾) to generatetruncated orthonormal basis vector 135 a (U_(B) ⁽¹⁾) and truncatedorthonormal basis vector 135 b (U_(B) ⁽²⁾). For instance, the controller104 may truncate the orthonormal basis vectors 134 a, 134 b (U⁽¹⁾, U⁽²⁾)to achieve a truncation value in X and Y of 125. It is noted herein thatthe controller 104 may be configured to perform the low-rankapproximations without truncating the orthonormal basis vector 134 c(U⁽³⁾) for the die space/stack space in order to track as muchdie-to-die variation as possible. Accordingly, as shown in FIG. 5, thecontroller 104 may abstain from truncating the orthonormal basis vector134 c (U⁽³⁾) for the die space/stack space when generating the referencetensor 136 (and reference image frames) via low-rank approximations.Subsequently, the controller 104 may be configured to generate thereference tensor 136 (T_(B)) according to Equation 2:

T _(B) =S _(B) U _(B) ⁽¹⁾ U _(B) ⁽²⁾ U ⁽³⁾  (2)

It is contemplated herein that the low-rank approximation, representedas reference tensor 136 (T_(B)), may correspond to the target tensor 130and may include a stack of reference image frames corresponding to thetarget image frames 125. These reference tensors 136 (T_(B)) andreference image frames may exhibit the overall essence of the patternimagery on the sample 120 within each reference image frame, and may notcapture (e.g., omit) random effects such as shot noise and defectsignals. In this regard, the reference target images of the referencetensor 136 (T_(B)) may capture the essence of the background pattern ofthe sample 120, and may be formed based only on the original targetimage frames 125.

In particular, by performing a low-rank approximation (instead of afull-rank decomposition), embodiments of the present disclosure havebeen found to accurately estimate background patterns of the sample 120while avoiding die-to-die alignment errors and process variation errorsassociated with conventional inspection techniques. Furthermore, becausethe reference image frames may be generated directly from acquiredtarget image frames 125 a-125 n, embodiments of the present disclosuremay enable faster inspection and improve throughput.

It is noted herein that a single target image frame 125 could be usedthroughout method 200 to generate a reference tensor 136 (T_(B))including a single reference image frame. However, it is further notedherein that the use of multiple target image frames 125 to construct thetarget tensor 130 (across either multiple die or multiple cells) mayreinforce the background pattern representation of the sample 120 atissue, and may thereby improve the estimation of the true pattern withinthe generated reference image frames.

It is further noted herein that the granularity of background estimation(e.g., coarse estimations vs. fine estimations) may generate a trade-offbetween background suppression and defect signal suppression.Accordingly, proper selection of the truncation rank used for thelow-rank approximations is a crucial step to obtaining accurate,high-quality reference tensors 136 (T_(B)) and reference image frames.Accordingly, in some embodiments, the controller 104 may be configuredto determine the truncation rank used for the low-rank approximations byoptimizing a signal-to-noise ration (SNR) of T−T_(B). In embodiments,the controller 104 may optimize the SNR of T−T_(B) by using knowndefects as part of a recipe setup, or by using synthesized defects.

In a step 208, one or more differences are identified between the one ormore target image frames 125 and the one or more reference image frames.This may be further understood with reference to FIGS. 6A-6C.

FIG. 6A illustrates a target image frame 125 c of a target tensor 130(T), in accordance with one or more embodiments of the presentdisclosure. FIG. 6B illustrates a reference image frame 135 c of areference tensor 136 (T_(B)), in accordance with one or more embodimentsof the present disclosure. FIG. 6C illustrates a difference image frame155 c, in accordance with one or more embodiments of the presentdisclosure.

In some embodiments, the controller 104 may be configured to identifyone or more differences by subtracting the reference image frames 135from the target image frames 125. In this regard, the controller 104 maybe configured to generate a difference tensor including one or moredifference image frames 155 by subtracting the reference image frames145 of the reference tensor 136 (T_(B)) from the target image frames 125of the target tensor 130 (T) (e.g., T−T_(B)). For example, FIG. 6Aillustrates a third target image frame 125 c of a target tensor 130, andFIG. 6B illustrates a third reference image frame 135 c of a referencetensor 136 (T_(B)) corresponding to the third target image frame 125 c.In this example, the controller 104 may be configured to generate athird reference image frame 155 c by subtracting the third referenceimage frame 135 c from the third target image frame 125 c. Thecontroller 104 may be configured to store generated difference tensorsand/or difference image frames 155 in memory 108. Subsequently, thecontroller 104 may be configured to identify one or more differencesbetween the target image frames 125 and the reference image frames 135.

As shown in FIGS. 6A-6C, subtraction of reference image frames 145 fromtarget image frames 125 should reveal any random components within theimages, including any defects. For instance, by subtracting theestimated background structure of the reference image frame 145 c fromthe target image frame 125 c, a defect 137 within the target image frame125 c may be clearly shown in the generated difference image frame 155c. By removing the background structure (e.g., subtracting referenceimage frames 145), defects 137 within the target image frames 125 may beclearly revealed.

FIG. 7A illustrates a difference image frame 165 generated by aconventional “die-to-die” or “cell-to-cell” inspection technique, andFIG. 7B illustrates a difference image frame 175 generated by aconventional “die-to-median die” or “cell-to-median cell” inspectiontechnique.

By comparing the difference image frames 165, 175 of FIGS. 7A and 7B tothe difference image frame 155 c in FIG. 6C, it may be appreciated thatembodiments of the present disclosure may enable the production ofhigher quality difference images. In particular, for this example, itwas found that embodiments of the present disclosure were able toachieve higher SNR values within the generated difference images ascompared to conventional inspection techniques which utilize the samedifference filter (diff filter).

In a step 210, one or more characteristics of the sample 120 aredetermined based on the one or more identified differences. For example,the controller 104 may be configured to determine one or morecharacteristics of the sample 120 based on one or more characteristicsof the one or more generated difference image frames 155. The controller104 may be configured to determine any characteristics of the sample 120known in the art including, but not limited to, defects (e.g., defectlocation, defect type), measurements (e.g., critical dimensions), andthe like.

In embodiments, the controller 104 may be configured to selectivelyadjust one or more process tools based on the determined characteristicsof the sample 120. For example, in some embodiments, the system 100 mayfurther include one or more process tools. The process tools may includeany process tools known in the art including, but not limited to, alithography tool, an etching tool, a deposition tool, and the like. Inthis example, the controller 104 may be configured to generate one ormore control signals configured to selectively adjust one or morecharacteristics of one or more process tools based on the one or moredetermined characteristics of the sample 120. In this regard, thecontroller 104 may be configured to initiate feedforward and/or feedbackcontrol loops in order to selectively adjust various steps of asemiconductor device fabrication process.

In some embodiments, the controller 104 may be further configured tode-noise the target tensor 130/target image frames 125 prior tocomparison with the reference tensor 136 (T_(B))/reference image frames145. This may be further understood with reference to FIG. 8.

FIG. 8 illustrate a flowchart for performing inspection using tensordecomposition processes and de-noising processes of a target tensor 130(T), in accordance with one or more embodiments of the presentdisclosure.

As shown in the lower path of FIG. 8, the controller 104 may beconfigured to generate a reference tensor 136 (T_(B)) includingreference image frames 145 based on a target tensor 130 (T) generatedbased on target image frames 125, as discussed previously herein withrespect to FIG. 2-6C. In additional and/or alternative embodiments, thecontroller 104 may be configured to perform an additional set ofdecomposition processes on the target tensor 130 (T) in order to form ade-noised target tensor 138.

For example, as shown in the upper path of FIG. 8 and similarlydescribed previously herein, the controller 104 may be configured toperform a set of one or more decomposition processes on the targettensor 130 and further perform one or more high-rank approximations togenerate a de-noised target tensor 138 (T_(N)). In embodiments, thede-noised target tensor 138 (T_(N)) may include one or more de-noisedtarget image frames corresponding to the target image frames 125 a-125n. The controller 104 may be configured to store the de-noised targettensor 138 (T_(N)) and de-noised target image frames in memory 108. Itis noted herein that any discussion associated with the decompositionprocesses and approximations of FIGS. 2-6C may be regarded as applyingto the decomposition processes and approximations of FIG. 8, unlessnoted otherwise herein.

Continuing with reference to FIG. 8, after forming the de-noised targettensor 138 (T_(N)) and the reference tensor 136 (T_(B)), the controller104 may be configured to identify one or more characteristics of thesample 120 by comparing the de-noised target tensor 138 (T_(N)) and thereference tensor 136 (T_(B)). For example, the controller 104 may beconfigured to identify one or more differences between the one or morede-noised target image frames and the one or more reference image frames145 by subtracting the reference tensor 136 (T_(B)). from the de-noisedtarget tensor 138 (T_(N)) to form a difference tensor 140 (T_(N)−T_(B)).Subsequently, the controller 104 may determine one or morecharacteristics of the sample 120 based on difference image frames 155of the difference tensor 140 (T_(N)−T_(B)).

It is contemplated herein that the system and method of the presentdisclosure may reduce noise experienced from using measured referenceimages constructed from adjacent die in a conventional die-to-diereference die subtraction. Additionally, the system and method of thepresent disclosure may avoid process variation error introduced byadjacent reference die by tracking process variations within the targetimage frames 125 a-125 n via low-rank approximations. The reduction ofprocess variation error has been found to be especially valuable nearthe edges of a sample 120. Furthermore, due to the fact that thereference image frames 145 are generated directly from the target imageframes 125, the system and method of the present disclosure may avoiddie-to-die alignment errors between the target die and adjacentreference die. Finally, decomposition processes may be used to ne-noisethe target image frames, further improving the determination andidentification of characteristics of a sample 120.

As noted previously herein, using conventional inspection techniques,defect detection on a sample 120 may be highly dependent on the qualityof the acquired difference images. Due to process variation, test dieand reference die could be vastly different, which may result insignificant pattern noise within the difference images. If not removed,this pattern noise within the difference images may hinder the abilityof conventional inspection systems to detect small defects on the sample120. Utilizing reference ide for multiple die rows (a common practicefor mask inspection) may further reduce the effectiveness of defectdetection.

Additionally, the effectiveness of conventional inspection techniquesutilizing target images and reference images hinges on the assumptionthat some reference die resemble the target die. However, there is noguarantee that every sample 120 will include reference die which willresemble the target die. Additionally, there could be multiplestructures on the target die, with some structures resembling those of areference die, and others not. This mis-matching of target structuresmay create pattern artifacts on the difference images, furtherinhibiting the utility of conventional inspection techniques.

Accordingly, additional and/or alternative embodiments of the presentdisclosure are directed to the application of decomposition andapproximation processes on difference images directly. This may befurther understood with reference to FIS. 9 and 10.

FIG. 9 illustrate a flowchart of a method 900 for performing inspectionusing singular value decomposition (SVD) processes, in accordance withone or more embodiments of the present disclosure. It is noted hereinthat the steps of method 900 may be implemented all or in part by system100. It is further recognized, however, that the method 900 is notlimited to the system 100 in that additional or alternative system-levelembodiments may carry out all or part of the steps of method 900. It isfurther noted herein that any discussion associated with method 200illustrated in FIGS. 2-8 may be regarded as applying to method 900,unless noted otherwise herein.

In a step 902, one or more difference image frames of a sample areacquired. For example, FIG. 10 illustrates a flowchart of a method forperforming inspection using singular value decomposition (SVD)processes, in accordance with one or more embodiments of the presentdisclosure. As shown in step 1002 of FIG. 10, a controller 104 may beconfigured to acquire one or more difference image frames of a sample102. The one or more difference images may be acquired from any sourceknown in the art including, but not limited to, the inspectionsub-system 102, memory, a network, and the like.

In some embodiments, the one or more difference image frames may includeone or more difference image frames which are based on and/or generatedfrom one or more target image frames and one or more reference imageframes. For example, as previously shown and described in FIGS. 6A-6C,the one or more difference image frames may be generated by subtractingreference image frames from target image frames. In embodiments, thecontroller 104 may be configured to store the acquired difference imagesand difference image frames in memory 108.

In a step 904, one or more stacked difference images are generated. Forexample, as shown in steps 1004 and 1006 of FIG. 10, the one or moreacquired difference image frames may be stacked and/or compiled togenerate one or more stacked difference images (d_(stk)(x, y)). Inembodiments, the stacked difference images (d_(stk)(x, y)) may containresidual pattern noise. The controller 104 may store the stackeddifference images (d_(stk)(x, y)) in memory 108.

In a step 906, a set of one or more singular value decomposition (SVD)processes are performed on the one or more stacked difference images(d_(stk)(x, y)) to form a set of one or more singular vectors. Forexample, as shown in step 1008, the controller 104 may be configured toperform one or more SVD processes on the stacked difference images(d_(stk)(x, y)) to form a set of one or more singular vectors. In SVDprocesses, an image (e.g., stacked difference image (d_(stk)(x, y))) iscomposed of multiple singular vectors, which correspond to differentfeatures of the image. Through SVD, singular vectors corresponding tohigh-ranked information of the image receive a higher singular value,and vice versa. In embodiments, the controller 104 is configured tostore the singular vectors in memory 108.

In a step 908, at least one singular vector of the set of one or moresingular vectors are selectively removed and/or modified in order togenerate a modified set of one or more singular vectors. It is notedherein that pattern noise may typically appear within the high-rankedvectors of the stacked difference image due to the fact that patternnoise is generally a high-ranged image. A pixel of an ideal differenceimage may be generated forma gaussian distribution, in which allsingular vectors are given similar weights. It should be noted that, inreality, pixels from difference images come from a correlated Gaussiandistribution due to the point spread function (PSF). In effect, weightsof singular values may fade or degrade over time. Accordingly, in orderto remove pattern noise, the controller 104 may be configured totruncate (selectively remove and/or modify) one or more singular vectorsof the set of singular vectors of the stacked difference image (d_(stk)(x, y)) in order to generate a modified set of one or more singularvectors.

In step 910, a modified stacked difference image is generated based onthe modified set of one or more singular vectors. For example, thecontroller 104 may be configured to reconstruct the decomposed stackeddifference image (d_(stk) (x, y)) as a high-order stacked differenceimage (d_(stk) ^(′)(x, y)) based on the modified set of one or moresingular vectors (e.g., set of remaining, non-truncated singularvectors). For instance, the controller 104 may be configured to generatethe high-order stacked difference image using the first k number ofsingular vectors. In this regard, the controller 104 may be configuredto reconstruct the stacked difference image (d_(stk)(x, y)) bytruncating one or more singular vectors. As noted previously herein,pattern noise may typically appear within the high-ranked vectors of thestacked difference image. Accordingly, by subtracting the effects ofhigh-ranked vectors (e.g., subtracting high-order stacked differenceimage (d_(stk) ^(′)(x, y))) from the original stacked difference image(d_(stk)(x, y)), the effects of high-order singular vectors may beremoved, thereby removing effects of pattern noise.

In embodiments, the controller 104 may be configured to perform one ormore truncated SVD processes (tSVD) in order to split the stackeddifference images (d_(stk)(x, y)) into multiple rectangular segments. Itis contemplated herein that truncating singular vectors and splittingimage frames via SVD and/or tSVD processes may enable significantthroughput improvements. In particular, it has been found that arelationship between an optimal truncation number and image variance maybe expresses according to Equation 3:

$\begin{matrix}{k_{opt} = \frac{\sigma^{2}}{K}} & (3)\end{matrix}$

wherein k_(opt) defines an optimal truncation number, σ² defines thevariance of a stacked difference image, and K defines an empiricallydetermined constant. In this regard, the number of singular vectors tobe truncated (e.g., k_(opt)) may be determined according to Equation 3.

In a step 912, one or more characteristics of the sample 120 aredetermined based on the modified stacked difference image (d_(clean)(x,y)). For example, the controller 104 may be configured to determine oneor more characteristics of the sample 120 based on one or morecharacteristics of the one or more modified stacked difference image(d_(clean)(x, y)). The controller 104 may be configured to determine anycharacteristics of the sample 120 known in the art including, but notlimited to, defects (e.g., defect location, defect type), measurements(e.g., critical dimensions), and the like.

One skilled in the art will recognize that the herein describedcomponents (e.g., operations), devices, objects, and the discussionaccompanying them are used as examples for the sake of conceptualclarity and that various configuration modifications are contemplated.Consequently, as used herein, the specific exemplars set forth and theaccompanying discussion are intended to be representative of their moregeneral classes. In general, use of any specific exemplar is intended tobe representative of its class, and the non-inclusion of specificcomponents (e.g., operations), devices, and objects should not be takenlimiting.

With respect to the use of substantially any plural and/or singularterms herein, those having skill in the art can translate from theplural to the singular and/or from the singular to the plural as isappropriate to the context and/or application. The varioussingular/plural permutations are not expressly set forth herein for sakeof clarity.

The herein described subject matter sometimes illustrates differentcomponents contained within, or connected with, different othercomponents. It is to be understood that such depicted architectures aremerely exemplary, and that in fact many other architectures may beimplemented which achieve the same functionality. In a conceptual sense,any arrangement of components to achieve the same functionality iseffectively “associated” such that the desired functionality isachieved. Hence, any two components herein combined to achieve aparticular functionality can be seen as “associated with” each othersuch that the desired functionality is achieved, irrespective ofarchitectures or intermedial components. Likewise, any two components soassociated can also be viewed as being “operably connected,” or“operably coupled,” to each other to achieve the desired functionality,and any two components capable of being so associated can also be viewedas being “operably couplable,” to each other to achieve the desiredfunctionality. Specific examples of operably couplable include but arenot limited to physically mateable and/or physically interactingcomponents, and/or wirelessly interactable, and/or wirelesslyinteracting components, and/or logically interacting, and/or logicallyinteractable components.

In some instances, one or more components may be referred to herein as“configured to,” “configurable to,” “operable/operative to,”“adapted/adaptable,” “able to,” “conformable/conformed to,” etc. Thoseskilled in the art will recognize that such terms (e.g., “configuredto”) can generally encompass active-state components and/orinactive-state components and/or standby-state components, unlesscontext requires otherwise.

While particular aspects of the present subject matter described hereinhave been shown and described, it will be apparent to those skilled inthe art that, based upon the teachings herein, changes and modificationsmay be made without departing from the subject matter described hereinand its broader aspects and, therefore, the appended claims are toencompass within their scope all such changes and modifications as arewithin the true spirit and scope of the subject matter described herein.It will be understood by those within the art that, in general, termsused herein, and especially in the appended claims (e.g., body of theappended claims) are generally intended as “open” terms (e.g., the term“including” should be interpreted as “including but not limited to,” theterm “having” should be interpreted as “having at least,” the term“includes” should be interpreted as “includes but is not limited to,”etc.). It will be further understood by those within the art that if aspecific number of an introduced claim recitation is intended, such anintent will be explicitly recited in the claim, and in the absence ofsuch recitation no such intent is present. For example, as an aid tounderstanding, the following appended claims may contain usage of theintroductory phrases “at least one” and “one or more” to introduce claimrecitations. However, the use of such phrases should not be construed toimply that the introduction of a claim recitation by the indefinitearticles “a” or “an” limits any particular claim containing suchintroduced claim recitation to claims containing only one suchrecitation, even when the same claim includes the introductory phrases“one or more” or “at least one” and indefinite articles such as “a” or“an” (e.g., “a” and/or “an” should typically be interpreted to mean “atleast one” or “one or more”); the same holds true for the use ofdefinite articles used to introduce claim recitations. In addition, evenif a specific number of an introduced claim recitation is explicitlyrecited, those skilled in the art will recognize that such recitationshould typically be interpreted to mean at least the recited number(e.g., the bare recitation of “two recitations,” without othermodifiers, typically means at least two recitations, or two or morerecitations). Furthermore, in those instances where a conventionanalogous to “at least one of A, B, and C, etc.” is used, in generalsuch a construction is intended in the sense one having skill in the artwould understand the convention (e.g., “a system having at least one ofA, B, and C” would include but not be limited to systems that have Aalone, B alone, C alone, A and B together, A and C together, B and Ctogether, and/or A, B, and C together, etc.). In those instances where aconvention analogous to “at least one of A, B, or C, etc.” is used, ingeneral such a construction is intended in the sense one having skill inthe art would understand the convention (e.g., “a system having at leastone of A, B, or C” would include but not be limited to systems that haveA alone, B alone, C alone, A and B together, A and C together, B and Ctogether, and/or A, B, and C together, etc.). It will be furtherunderstood by those within the art that typically a disjunctive wordand/or phrase presenting two or more alternative terms, whether in thedescription, claims, or drawings, should be understood to contemplatethe possibilities of including one of the terms, either of the terms, orboth terms unless context dictates otherwise. For example, the phrase “Aor B” will be typically understood to include the possibilities of “A”or “B” or “A and B.”

With respect to the appended claims, those skilled in the art willappreciate that recited operations therein may generally be performed inany order. Also, although various operational flows are presented in asequence(s), it should be understood that the various operations may beperformed in other orders than those which are illustrated, or may beperformed concurrently. Examples of such alternate orderings may includeoverlapping, interleaved, interrupted, reordered, incremental,preparatory, supplemental, simultaneous, reverse, or other variantorderings, unless context dictates otherwise. Furthermore, terms like“responsive to,” “related to,” or other past-tense adjectives aregenerally not intended to exclude such variants, unless context dictatesotherwise.

Although particular embodiments of this invention have been illustrated,it is apparent that various modifications and embodiments of theinvention may be made by those skilled in the art without departing fromthe scope and spirit of the foregoing disclosure. It is believed thatthe present disclosure and many of its attendant advantages will beunderstood by the foregoing description, and it will be apparent thatvarious changes may be made in the form, construction and arrangement ofthe components without departing from the disclosed subject matter orwithout sacrificing all of its material advantages. The form describedis merely explanatory, and it is the intention of the following claimsto encompass and include such changes. Accordingly, the scope of theinvention should be limited only by the claims appended hereto.

What is claimed:
 1. A sample characterization system, comprising: acontroller communicatively coupled to an inspection sub-system, thecontroller including one or more processors configured to execute a setof program instructions stored in memory, the set of programinstructions configured to cause the one or more processors to: acquireone or more target image frames of a sample; generate a target tensorwith the one or more acquired target image frames; perform a first setof one or more decomposition processes on the target tensor to formgenerate one or more reference tensors including one or more referenceimage frames; identify one or more differences between the one or moretarget image frames and the one or more reference image frames; anddetermine one or more characteristics of the sample based on the one ormore identified differences.
 2. The system of claim 1, wherein the firstset of one or more decomposition processes comprise a Tuckerdecomposition process.
 3. The system of claim 2, wherein the Tuckerdecomposition process comprises a multilinear singular valuedecomposition process.
 4. The system of claim 1, wherein the controlleris configured to perform the first set of one or more decompositionprocesses on the target tensor using a first orthonormal basis vectorfor a column space of the target tensor, a second orthonormal basisvector for a row space of the target tensor, and a third orthonormalbasis vector for a stack space of the target tensor.
 5. The system ofclaim 1, wherein the controller is configured to generate the one ormore reference tensors by: performing one or more low-rankapproximations of a core tensor used to carry out the one or moredecomposition processes.
 6. The system of claim 5, wherein thecontroller is configured to perform the one or more low-rankapproximations by truncating at least a portion of the core tensor. 7.The system of claim 5, wherein the controller is configured to performthe one or more low-rank approximations by truncating one or moreorthonormal basis vectors used for the one or more decompositionprocesses.
 8. The system of claim 1, wherein the one or more identifiedcharacteristics comprise a defect of the sample.
 9. The system of claim1, wherein the controller is further configured to: generate one or morecontrol signals configured to selectively adjust one or morecharacteristics of one or more process tools based on the one or moredetermined characteristics.
 10. The system of claim 1, wherein thecontroller is further configured to: perform a second set of one or moredecomposition processes on the target tensor to form a de-noised coretensor; and perform one or more high-rank approximations on thede-noised core tensor to generate a de-noised target tensor, thede-noised target tensor including one or more de-noised target imageframes.
 11. The system of claim 10, wherein the controller is furtherconfigured to: identify one or more differences between the one or morede-noised target image frames and the one or more reference imageframes; and determine one or more characteristics of the sample based onthe one or more identified differences.
 12. A method for characterizinga sample, comprising: acquiring one or more target image frames of asample; generating a target tensor with the one or more acquired targetimage frames; performing a first set of one or more decompositionprocesses on the target tensor to generate one or more reference tensorsincluding one or more reference image frames; identifying one or moredifferences between the one or more target image frames and the one ormore reference image frames; and determining one or more characteristicsof the sample based on the one or more identified differences.
 13. Themethod of claim 12, wherein the first set of one or more decompositionprocesses comprise a Tucker decomposition process.
 14. The method ofclaim 13, wherein the Tucker decomposition process comprises amultilinear singular value decomposition process.
 15. The method ofclaim 12, wherein performing the first set of one or more decompositionprocesses on the target tensor comprises: performing the first set ofone or more decomposition processes on the target tensor using a firstorthonormal basis vector for a row space of the target tensor, a secondorthonormal basis vector for a column space of the target tensor, and athird orthonormal basis vector for a stack space of the target tensor.16. The method of claim 12, wherein generating one or more referencetensors including one or more reference image frames based on a coretensor comprises: performing one or more low-rank approximations of thecore tensor used to carry out the one or more decomposition processes.17. The method of claim 16, wherein performing one or more low-rankapproximations of the core tensor comprises: truncating at least aportion of the core tensor.
 18. The method of claim 16, whereinperforming one or more low-rank approximations of the core tensorcomprises: truncating one or more orthonormal basis vectors used for theone or more decomposition processes.
 19. The method of claim 12, whereinthe one or more identified characteristics comprise a defect of thesample.
 20. The method of claim 12, further comprising: generating oneor more control signals configured to selectively adjust one or morecharacteristics of one or more process tools based on the one or moredetermined characteristics.
 21. The method of claim 12, furthercomprising: performing a second set of one or more decompositionprocesses on the target tensor to form a de-noised core tensor; andperforming one or more high-rank approximations on the de-noised coretensor to generate a de-noised target tensor, the de-noised targettensor including one or more de-noised target image frames.
 22. Themethod of claim 21, further comprising: identifying one or moredifferences between the one or more de-noised target image frames andthe one or more reference image frames; and determining one or morecharacteristics of the sample based on the one or more identifieddifferences.
 23. A sample characterization system, comprising: acontroller communicatively coupled to an inspection sub-system, thecontroller including one or more processors configured to execute a setof program instructions stored in memory, the set of programinstructions configured to cause the one or more processors to: acquireone or more difference image frames of a sample, the one or moredifference image frames based on one or more target image frames and oneor more reference image frames; generate one or more stacked differenceimages with the one or more acquired difference image frames; perform aset of one or more singular value decomposition (SVD) processes on theone or more stacked difference images to form a set of one or moresingular vectors; selectively modify at least one singular vector of theset of one or more singular vectors to generate a modified set of one ormore singular vectors; generate a modified stacked difference imagebased on the modified set of one or more singular vectors; and determineone or more characteristics of the sample based on the modified stackeddifference image.
 24. The system of claim 23, wherein the controller isconfigured to determine one or more characteristics of the sample basedon a gray level of one or more pixels of the modified stacked differenceimage.
 25. The system of claim 23, wherein the controller is configuredto selectively modify at least one singular vector of the set of one ormore singular vectors by: truncating a first k number of singularvectors of the first set of one or more singular vectors.
 26. The systemof claim 25, wherein k is determined according to the equation k=σ²/K,wherein σ² comprises a variance value of the one or more stackeddifference images and K comprises an empirically determined constant.27. The system of claim 23, wherein the one or more identifiedcharacteristics comprise a defect of the sample.
 28. The system of claim23, wherein the controller is further configured to: generate one ormore control signals configured to selectively adjust one or morecharacteristics of one or more process tools based on the one or moredetermined characteristics.
 29. A method for characterizing a sample,comprising: acquiring one or more difference image frames of a sample,the one or more difference image frames based on one or more targetimage frames and one or more reference image frames; generating one ormore stacked difference images with the one or more acquired differenceimage frames; performing a set of one or more singular valuedecomposition (SVD) processes on the one or more stacked differenceimages to form a set of one or more singular vectors; selectivelymodifying at least one singular vector of the set of one or moresingular vectors to generate a modified set of one or more singularvectors; generating a modified stacked difference image based on themodified set of one or more singular vectors; and determining one ormore characteristics of the sample based on the modified stackeddifference image.